A connected sum formula for the SU(3) Casson invariant

We provide a formula for the SU(3) Casson invariant for 3-manifolds given as the connected sum of two integral homology 3-spheres.Comment: 14 page

The SU(3) Casson Invariant for Integral Homology 3-Spheres

We derive a gauge theoretic invariant of integral homology 3-spheres which counts gauge orbits of irreducible, perturbed flat SU(3) connections with sign given by spectral flow. To compensate for the dependence of this sum on perturbations, the invariant includes contributions from the reducible, perturbed flat orbits. Our formula for the correction term generalizes that given by Walker in his extension of Casson's SU(2) invariant to rational homology 3-spheres.Comment: 63 pages, 2 figures, to appear in J. Diff. Geo

The Integer Valued SU(3) Casson Invariant for Brieskorn spheres

We develop techniques for computing the integer valued SU(3) Casson invariant. Our method involves resolving the singularities in the flat moduli space using a twisting perturbation and analyzing its effect on the topology of the perturbed flat moduli space. These techniques, together with Bott-Morse theory and the splitting principle for spectral flow, are applied to calculate the invariant for all Brieskorn homology spheres.Comment: 50 pages, 3 figure

Gauge Theoretic Invariants of, Dehn Surgeries on Knots

New methods for computing a variety of gauge theoretic invariants for homology 3-spheres are developed. These invariants include the Chern-Simons invariants, the spectral flow of the odd signature operator, and the rho invariants of irreducible SU(2) representations. These quantities are calculated for flat SU(2) connections on homology 3-spheres obtained by 1/k Dehn surgery on (2,q) torus knots. The methods are then applied to compute the SU(3) gauge theoretic Casson invariant (introduced in [H U Boden and C M Herald, The SU(3) Casson invariant for integral homology 3--spheres, J. Diff. Geom. 50 (1998) 147-206]) for Dehn surgeries on (2,q) torus knots for q=3,5,7 and 9.Comment: Version 3: minor corrections from version 2. Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper6.abs.htm

Statistical Properties of the GALEX/SDSS matched source catalogs, and classification of the UV sources

We use the Galaxy Evolution Explorer (GALEX) Medium and All-Sky-Imaging Survey (MIS & AIS) data from the first public data release (GR1), matched to the Sloan Digital Sky Survey (SDSS) DR3 catalog, to perform source classification. The GALEX surveys provide photometry in far- and near-UV bands and the SDSS in five optical bands (u,g,r,i,z). The GR1/DR3 overlapping areas are 363[83]deg^2 for the GALEX AIS[MIS], for sources within the 0.5deg central area of the GALEX fields. Our sample covers mostly |b|>30deg galactic latitudes. We present statistical properties of the GALEX/SDSS matched sources catalog, containing >2x10^6 objects detected in at least one UV band. We classify the matched sources by comparing the seven-band photometry to model colors constructed for different classes of astrophysical objects. For sources with photometric errors <0.3 mag, the corresponding typical AB-magnitude limits are m_FUV~21.5, m_NUV~22.5 for AIS, and m_FUV~24, m_NUV~24.5 for MIS. At AIS depth, the number of Galactic and extragalactic objects are comparable, but the latter predominate in the MIS. Based on our stellar models, we estimate the GALEX surveys detect hot White Dwarfs throughout the Milky Way halo (down to a radius of 0.04 R_sun at MIS depth), providing an unprecedented improvement in the Galactic WD census. Their observed surface density is consistent with Milky Way model predictions. We also select low-redshift QSO candidates, extending the known QSO samples to lower magnitudes, and providing candidates for detailed z~1 follow-up investigations. SDSS optical spectra available for a large subsample confirm the classification for the photometrically selected candidates with 97% purity for single hot stars, ~45%(AIS)/31%(MIS) for binaries containing a hot star and a cooler companion, and about 85% for QSOs.Comment: 33 pages, 11 figures, accepted for the GALEX special issue of ApJS. For a version with full resolution figures see http://dolomiti.pha.jhu.edu/publgoto.htm

Mortality and pulmonary complications in patients undergoing surgery with perioperative SARS-CoV-2 infection: an international cohort study

Background: The impact of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) on postoperative recovery needs to be understood to inform clinical decision making during and after the COVID-19 pandemic. This study reports 30-day mortality and pulmonary complication rates in patients with perioperative SARS-CoV-2 infection. Methods: This international, multicentre, cohort study at 235 hospitals in 24 countries included all patients undergoing surgery who had SARS-CoV-2 infection confirmed within 7 days before or 30 days after surgery. The primary outcome measure was 30-day postoperative mortality and was assessed in all enrolled patients. The main secondary outcome measure was pulmonary complications, defined as pneumonia, acute respiratory distress syndrome, or unexpected postoperative ventilation. Findings: This analysis includes 1128 patients who had surgery between Jan 1 and March 31, 2020, of whom 835 (74·0%) had emergency surgery and 280 (24·8%) had elective surgery. SARS-CoV-2 infection was confirmed preoperatively in 294 (26·1%) patients. 30-day mortality was 23·8% (268 of 1128). Pulmonary complications occurred in 577 (51·2%) of 1128 patients; 30-day mortality in these patients was 38·0% (219 of 577), accounting for 81·7% (219 of 268) of all deaths. In adjusted analyses, 30-day mortality was associated with male sex (odds ratio 1·75 [95% CI 1·28–2·40], p\textless0·0001), age 70 years or older versus younger than 70 years (2·30 [1·65–3·22], p\textless0·0001), American Society of Anesthesiologists grades 3–5 versus grades 1–2 (2·35 [1·57–3·53], p\textless0·0001), malignant versus benign or obstetric diagnosis (1·55 [1·01–2·39], p=0·046), emergency versus elective surgery (1·67 [1·06–2·63], p=0·026), and major versus minor surgery (1·52 [1·01–2·31], p=0·047). Interpretation: Postoperative pulmonary complications occur in half of patients with perioperative SARS-CoV-2 infection and are associated with high mortality. Thresholds for surgery during the COVID-19 pandemic should be higher than during normal practice, particularly in men aged 70 years and older. Consideration should be given for postponing non-urgent procedures and promoting non-operative treatment to delay or avoid the need for surgery. Funding: National Institute for Health Research (NIHR), Association of Coloproctology of Great Britain and Ireland, Bowel and Cancer Research, Bowel Disease Research Foundation, Association of Upper Gastrointestinal Surgeons, British Association of Surgical Oncology, British Gynaecological Cancer Society, European Society of Coloproctology, NIHR Academy, Sarcoma UK, Vascular Society for Great Britain and Ireland, and Yorkshire Cancer Research